47.  The function f : [0, 3]  [1, 29], defined by f(x) = 2x 3   15x 2 + 36x + 1, is

(A)  one-one and onto  (B) onto but not one-one

(C) one-one but not onto  (D) neither one-one nor onto

the given function is

differentiating the function wrt x,

thus the function is increasing from 0<x<2,

and then decreasing from x=2 to x=3

it is not monotonically increasing or decreasing.

thus the function is not one-one.

now we will check the image of the function at critical points.


therefore the function is onto, but not one-one.

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